Postulates of Congruent Triangle

In this section we will discuss postulates of congruent triangles .

Two triangles are congruent if and only if there exists a correspondence between their vertices such that the corresponding sides and corresponding angles of two triangles are equal.
To show that two triangles are congruent, it is not necessary to show that all six pairs of corresponding parts are equal. The following postulates and theorems are the most common methods for proving that triangles are congruent (or equal).

Postulates of Triangles

• Side Angle Side Postulate -> If two sides and the included angle of a triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Example : In ΔMNO and ΔDEF,if MN =DE; ∠N = ∠E and NO = EF then ΔABC ≅ΔPQR by SAS postulate.

• Side Side Side Postulate -> If the three sides of a triangle are congruent to the three sides of another triangle, then the two triangles are congruent.Example : In ΔABC and ΔPQR,if AB =PQ; BC = QR and AC = PR then ΔABC ≅ΔPQR by SSS postulate.

• Angle Angle Side Postulate -> If two angles and a non-included side of a triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.Example : In ΔDEF and ΔXYZ,if ∠D =∠x, ∠E = ∠y and EF = YZ then ΔDEF ≅ΔXYZ by AAS postulate.

• Angle Side Angle Postulate -> If two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.Example : In ΔABC and ΔPQR,if ∠A =∠P ; AB = PQ and ∠B = ∠Q then ΔABC ≅ΔPQR by ASA postulate.

• HL postulate(Hypotenuse – Leg OR RHS) -> If any two right angles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.Example : In ΔABC and ΔDEF are right angled triangle at B and E respectively.If AC = DF and BC = EF then ΔABC ≅ΔDEF by HL (RHS) postulate.Triangles